Your car appears similar to my 1987 300E so I'm going to suggest that the symtoms you describe sound like cracked solder joints on the cars fuel relay board.
If so the condition is activated by heat that causes the cracks to expand and lose contact. The cracks themselves are caused by the weight of the little electro magnets that operate sets of points that are mounted on the circuit board. Vibrations over time cause the solder to crack at the pins where the magnets are connected to the board. Look on the back of the board and you may see circular hairline cracks around the some of the pins.
If so resolder or replace fuel relay. My relay looks about the size of a pack of cigarettes and is a black plastic box. The bottom will slide out of the box to expose the circuit board. It is located on the passenger side engine compartment behind the plastic panel that sits under windshield area.
1993 190E 2.3
2000 Toyota 4x4 Tundra